4.3 Comparison between permanent magnet design and electromagnet design
Following table shows a comparison between permanent magnet design versus
electromagnet design. Neo magnet design has smallest overall radius.
Magnet
Ferrite magnet
Neo magnet
Electromagnet
Magnet radius
16.4"
6.1"
10"
Pole tip radius
2 cm
2 cm
2 cm
Ferrite magnet
Neo magnet
Electromagnet
15.5"
6.5"
9.8"
3 cm
3 cm
3 cm
56
Figure 4-3. Electromagnet quadrupole design (3 cm pole tip radius)
55
Pole tip field vs. current
10000
9000
8000
pole tip field
7000
6000
5000
4000
3000
2000
1000
0
0
1000
2000
3000
4000
5000
6000
7000
8000
Amp turns
Figure 4-2. Pole tip field versus coil Amp turns (2 cm pole tip radius)
54
9000
Figure 4-1. Electromagnet quadrupole design (2 cm pole tip radius)
53
4.2 Electromagnet design
A conventional electromagnet design has also been tried for the NLC Damping Ring
Quadrupole. Figure 4-1 shows an electromagnet quadrupole design using a circular outer iron
core so we can make direct comparisons with the pms, we would not necessarily make a
circular iron core for any of these designs. The pole tip radius is 2 cm and the outer radius of
the magnet is 10”. In this design, there are total 22 turns of 0.255” square hollow copper
conductor in 2 layers of 11 turns each in each coil. The input current is 347 amps and the
current density is 605.5 Amps/cm2. The approximate coil length is 60 ft. The coil hole
diameter is 0.125” and the calculated coil power is 1.231 kW. Based on these data, the
amount of water flow is obtained from curves generated from the Williams and Hazen
formula. With 4 cooling circuits per quad, the water flow is 0.345 gal/min and the temperature
difference between in the inlet of coil and in the outlet of the coil can be calculated as
∆T =
3.8 × 1.231
=13.6 oC
0.345
where 3.8 is a constant. This is well below our operating maximum delta T of 25 oC. Figure
4-2 shows pole tip field versus coil amp turns. It shows pretty much linear for the whole
region.
For 3 cm pole tip radius design, the input amp turns are 6800 Amp turns and the
current density is 659.4 Amps/cm2. The approximate coil length is 54 ft. The calculated coil
power is 1.317 kW. From the curve, the amount of water flow is 0.365 gal/min. Based on
these data, the temperature increase is calculated as 13.7 oC. Next table summarizes the
parameters and temperature rise for electromagnetic DR quads.
pole tip radius magnet radius
(cm)
(in)
coil turns
Amp turns
(Amps)
coil length coil hole diameter coil power
(ft)
(in)
(kW)
water flow
(gal/min)
temperature rise
o
( C)
2
10
22
7631.4
60
0.125
1.231
0.345
13.6
3
9.8
18
6800
54
0.125
1.317
0.365
13.7
52
IV. Electromagnet design and Comparison for NLC Damping Ring Quadrupole
4.1 Features
1). The magnet radius: 10” for 2 cm pole tip magnet and 9.8” for 3 cm pole tip magnet.
2). For 2 cm pole tip radius magnet:
Total current: 7631.4 Amp turns
Current density: 605.5 Amps/cm2
Number of coil turns: 22
Approximate coil length: 60 ft
Calculated coil power: 1.231 kW
Thickness of two layer coil: 0.596”
For 3 cm pole tip radius magnet:
Total current: 6800 Amp turns
Current density: 659.4 Amps/cm2
Number of coil turns: 18
Approximate coil length: 54 ft
Calculated coil power: 1.317 kW
Thickness of two layer coil: 0.596”
4). There is 5 cm space between the quadrupole magnet and the other magnet.
3). Temperature rise in the coil: 13.6 oC for 2 cm pole tip and 13.7 oC for 3 cm pole tip
pole tip radius magnet radius
(cm)
(in)
coil turns
Amp turns
(Amps)
coil length coil hole diameter coil power
(ft)
(in)
(kW)
water flow
(gal/min)
temperature rise
o
( C)
2
10
22
7631.4
60
0.125
1.231
0.345
13.6
3
9.8
18
6800
54
0.125
1.317
0.365
13.7
51
Figure 3-18. Neo quadrupole magnet in damping ring, demagnetization design II
(3 cm pole tip radius, 0.5” radius tuner, pole tip field=6.13 kG)
50
Figure 3-17. Neo quadrupole magnet in damping ring, demagnetization design I
(3 cm pole tip radius, 0.5” radius tuner, pole tip field=6.2 kG)
49
Figure 3-16. Neo quadrupole magnet in damping ring, demagnetization design II
(2 cm pole tip radius, 0.5” radius tuner, pole tip field=9.88 kG)
48
Figure 3-15. Neo quadrupole magnet in damping ring, demagnetization design I
(2 cm pole tip radius, 0.5” radius tuner, pole tip field=9.86 kG)
47
Integrated field
120000
integrated field (G-cm)
100000
80000
60000
40000
20000
0
0
2
4
6
8
10
gap between magnet and steel plate (in)
Figure 3-14. Integrated field at pole tip ( ∫ B pole tip dl )
(Without the end plate, the integrated field is 105 kG-cm.)
46
12
Figure 3-13. Adding an end plate on the magnet
45
Figure 3-12. Full model of Neo magnet
44
Figure 3-11. One eighth model of Neo magnet
43
Figure 3-10. Full model of Ferrite magnet
42
Figure 3-9. One eighth model of Ferrite magnet
41
Tuner torque for Neo magnet
300
torque (lb-in)
250
200
150
100
50
0
0
50
100
150
200
250
tuner angle (degree)
Figure 3-8. Tuner torque for Neo magnet
40
300
350
400
Figure 3-7. Neo quadrupole magnet for tuner torque calculation
39
Tuner torque for Ferrite magnet
450
400
torque (lb-in)
350
300
250
200
150
100
50
0
0
50
100
150
200
250
300
tuner angle
Figure 3-6. Tuner torque for Ferrite magnet
38
350
400
Figure 3-5. Ferrite quadrupole magnet for tuner torque calculation
37
Figure 3-4. Neo quadrupole magnet in damping ring
(3 cm pole tip radius, 0.5” radius tuner, pole tip field=6.11 kG)
36
Figure 3-3. Neo quadrupole magnet in damping ring
(2 cm pole tip radius, 0.5” radius tuner, pole tip field=9.74 kG)
35
Figure 3-2. Ferrite quadrupole magnet in damping ring
(3 cm pole tip radius, 1” radius tuner, pole tip field=6.51 kG)
34
Figure 3-1. Ferrite quadrupole magnet in damping ring
(2 cm pole tip radius, 1.13” radius tuner, pole tip field=10.4 kG)
33
value is zero at this location.) Design II is to cut the permanent magnet brick back to the
location where B = 1/4 Br. (see Figure 3-16)
In the following designs, a 12% end effect is added to the pole tip field strength based
on earlier 3-D TOSCA results. Figure 3-15 shows design I for 2 cm pole tip radius. 1.2” of the
wedge shaped magnet is cut. Figure 3-16 shows design II for 2 cm pole tip radius. In case of 3
cm pole tip radius, Figure 3-17 and 3-18 show design I and design II.
32
% which is thankfully less than that of Ferrite magnet, but nevertheless not a trivial
percentage.
3.6 Adding an End Plate on the Magnet - modeling a design feature of the FNAL Linac
PM Quad
To see if adding a steel end plate would help reduce the end effect, the following
calculations were carried out. An additional steel plate is added onto each end face of magnet
and three dimensional TOSCA calculation is performed to find out the end effects of the
magnet.
Figure 3-13 shows the flux plot for a model with an end plate added on the face of
magnet with a small gap. Several calculations are performed with different space between
magnet and end plate. Figure 3-14 shows integrated field ( ∫ Bdl ) along z direction, changing
the space between magnet and steel plate. As can be seen, as the steel plate is closer to the
magnet, there is more flux loss. Therefore, adding steel plate to the magnet does not reduce
the end effect. It generates more flux loss from the magnet.
More studies are pending on the end effect with adding an end plate onto the magnet.
3.7 Demagnetization in the permanent magnet bricks
In Figure 3-1, 3-2, 3-3 and 3-4, there are some demagnetization areas in the wedge
shaped permanent magnet bricks adjacent to the pole tip. In the demagnetized area of
permanent magnet brick, the overall field line direction is opposite to the desired field line
direction. New designs were done for Neo magnet quadrupole to avoid the demagnetization in
the permanent magnet bricks. In the new design, the demagnetized parts are removed.
Therefore, the whole dimension had to be increased to generate the same pole tip field
strength. There are two kinds of design for avoiding the demagnetization. Design I is to cut
the permanent magnet brick back to the demagnetization starting point; see Figure 3-15. (B
31
symmetrical at 45 degrees and 225 degrees of tuner angle because the Neo magnets on the
bottom and side are symmetric.
3.5.1 Three-dimensional modeling of DR quadrupoles.
Three dimensional models of the DR quads have been made using the TOSCA 3-D
program in order to calculate more precisely the end effect. Before applying the simulation of
3-d, a two dimensional TOSCA calculation is made to see whether the mesh generation and
other computation conditions are good or not. So, from the base plane, the whole magnet
shape is extruded in z-direction to a certain length of z value. A tangential boundary condition
is applied for top and base plane of the simulation. This method simulates an infinitely long
magnet in z-direction similar to the PANDIRA model. It is observed that there is 0.2 % field
strength difference between this TOSCA 2-d result and PANDIRA result for the same
FERRITE magnet at its pole tip location : The value of TOSCA result is 0.2 % higher than
that of PANDIRA. This is remarkably good agreement. Therefore, the mesh generation and
the other conditions in TOSCA are good enough to use it for a 3-d calculation. Three
dimensional computation is done by using this base plane geometry and conditions. The result
shows that the pole tip field strength in the center of the TOSCA 3-D magnet is 18.4 % lower
than that of PANDIRA result. This reduction in B at the pole tip is due to flux leaking out of
the ends – which the TOSCA program calculates. Figure 3-9 shows an one eighth model of
the 3-d Ferrite magnet and Figure 3-10 shows a full 3-d magnet. In this case, the one eighth
model is mirrored onto other section.
So, it turns out there is a significant end effect because the overall ferrite magnet
diameter is so large compared to its length. In order to compensate for this end effect (18.4
%), one needs to increase the goal field strength by 18.4 %. That means much larger magnet
is needed and much larger magnet produces much larger end effect. With this trend, the final
design of Ferrite magnet has very large radius. Figure 3-11 shows an one eighth model of Neo
magnet and Figure 3-12 shows a full Neo magnet. For Neo magnet case, the end effect is 10
30
3.5 End Effects
There is a field loss through the two end faces of the magnet. It is called the end effect
loss. Since PANDIRA program only calculates for two dimensional design, the following
method is used to compensate the end effect. To compensate for the end effect, the goal field
strength is increased by the same amount of field loss. From 3-D TOSCA result (to be
mentioned later), 18.4 % end effect is applied for a particular Ferrite magnet and 10% for a
Neo magnet.
Figure 3-1 shows a Ferrite magnet having 2 cm pole tip radius. In this magnet a 1.13 “
radius tuner is used to make ± 10 % field strength change at the pole tip. The required field
dg
quality is that
< 1 % at 80 % location of pole tip radius. To obtain this field quality,
g
shimming is used around the pole tip. It has 18.8” magnet radius and the maximum field is
10.4 kG. Figure 3-2 shows a Ferrite magnet having 3 cm pole tip radius. 1” radius tuner is
used for ± 10 % field strength change. No shimming is needed to improve the field quality.
Figure 3-3 shows a Neo magnet having 2 cm pole tip radius. Only 0.5” radius tuner is needed
to change the field by ± 10 % and shimming is needed to improve the field quality. The
magnet is only 6.5” radius magnet. It’s a quite small magnet compared to a Ferrite magnet
(Figure 3-1). Figure 3-4 shows a Neo magnet having 3 cm pole tip radius. Shimming is not
needed and 0.5” radius tuner is used. For Neo magnet, a fixture is needed for outer steel yoke
to keep the space for vacuum chamber.
Tuner torques are calculated for a Ferrite magnet (Figure 3-5). Figure 3-6 shows tuner
torques with respect to tuner angle. As can be seen in the figure, the value of maximum tuner
torque is very high. The torque values are not completely symmetric at 45 degrees and 225
degrees of tuner angle. It is because the Ferrite magnets on the bottom and side are not
symmetry. Figure 3-8 shows tuner torques for Neo magnet (Figure 3-7) with respect to tuner
angle. In this case, torque values are smaller than those of Ferrite magnet. Torque values are
29
Table 3-1. Damping ring layout from Andy Wolski
28
3.2 2-D Poisson for Permanent Magnets
There are two types of pole tip radius in the DR quadrupole magnet layout from Andy
Wolski (Table 3-1). One is 2 cm and the other is 3 cm. In the original layout, the magnets
have the effective lengths of 25 cm or 15 cm. The required pole tip fields are varied as the
required integrated gradient varies. A different approach was taken: a magnet with the highest
pole tip field strength is chosen as a base model, it had effective length of 25 cm and the
lengths of other magnets are changed to arrive at the required integrated strength.
3.3 Temperature Compensation Effects
Either Ferrite or Neodymium Iron Boron (“Neo”) is used for designing the magnets.
The designs are performed for 2 cm and 3 cm pole tip radius. In the magnet operation, to
offset field variations with temperature, special temperature compensation materials are used.
The detailed explanation of temperature compensation application is in section 1.2 (p.5). The
effect of the temperature compensating material is to make very large Ferrite magnets.
3.4 Tuners
There is another requirement : that the magnet can generate ± 10 % variation of field
strength at the pole tip. This effect is obtained by rotating a special Neo tuner. This ± 10 %
requirement makes tuner bigger and eventually the torque needed to rotate the tuner from its
preferred position to the +10% for example, gets ridiculously large.
27
Figure 3-18. Neo quadrupole magnet in damping ring, demagnetization design II
(3 cm pole tip radius, 0.5” radius tuner, pole tip field=6.13 kG)
26
Figure 3-17. Neo quadrupole magnet in damping ring, demagnetization design I
(3 cm pole tip radius, 0.5” radius tuner, pole tip field=6.2 kG)
25
Figure 3-16. Neo quadrupole magnet in damping ring, demagnetization design II
(2 cm pole tip radius, 0.5” radius tuner, pole tip field=9.88 kG)
24
Figure 3-15. Neo quadrupole magnet in damping ring, demagnetization design I
(2 cm pole tip radius, 0.5” radius tuner, pole tip field=9.86 kG)
23
III. Damping Ring Quadrupole Magnet Design (NLC)
3.1 Features and recommendations
Magnet Requirements
1). Requirements for quadrupole magnet for NLC damping ring are in Table 3-1.
Two types of pole tip radius: 2 cm and 3 cm
Effective lengths: 25 cm and 15 cm.
Required maximum field strength: 7958 G
Required tuning range: ± 10 %
Field quality: dg/g < 1 % at 80 % location of pole tip radius
Vacuum chamber space: 9 mm (7.5 mm minimum) => C shaped magnet
Models created in PANDIRA:
2). Ferrite and Neodymium Iron Boron (“Neo”) are used for the designs.
3). Ferrite magnet with shim (Figure 3-1, Figure 3-2) meets requirements.
Dimension for Figure 3-1: 2 cm pole tip radius, 18.8” radius magnet.
Dimension for Figure 3-2: 3 cm pole tip radius, 18.2” radius magnet.
4). Neo magnet with shim (Figure 3-3, Figure 3-4) meets requirements.
Dimension for Figure 3-3: 2 cm pole tip radius, 6.5” radius magnet.
Dimension for Figure 3-4: 3 cm pole tip radius, 7” radius magnet.
5). Torque for tuning rod is very high in Ferrite magnet.
6). Field clamp is tried but it doesn’t reduce the end effect.
7). Recommendations:
Figures 3-15 – 3-18 are duplicated here to show the recommended models that avoid
demagnetization in the permanent magnet. Radiation studies will help the choice of allowable
PM operation point along the demagnetization load line (Figure 3-15 vs. Figure 3-16, Figure
3-17 vs. Figure 3-18). The field qualities (dg/g) of models in Figure 3-15 – 3-18 are about 0.3
%. Again, Ferrite magnet has a too large an overall dimension. So, if radiation damage were
not a problem, or could be mitigated then we would recommend the Neo magnet.
22
Figure 2-2. Gradient dipole magnet
21
Combining equations (2.5), (2.6) and (2.7) produces
y pole
x =0
≡ hv = h p 1 +
(Vo B1′ )2
Bo
4
=
Vo
Bo
(2.8)
For h p =2 cm, B1′ =660.46 G/cm and Bo =12.01 kG, Vo can be solved by equation (2.8). By
equation (2.8), Vo =24161 G-cm. Using equation (2.5), the pole tip shape can be determined as
yp =
V o / Bo
2.012
=
1 − B1′ x / Bo 1 − 0.055 x
(2.9)
Using this pole tip shape, the gradient dipole magnet is designed. Figure 2-2 shows the
gradient dipole magnet and the field lines as predicted by POISSON. Maximum field
dB y
dB y
variation
is about 0.08 % at 1.6 cm circle of radius. The requirement of
is 0.3 %.
By
By
Therefore, this pole tip shape gives a good field quality. Adding shims around the pole tip
edges can make the magnet smaller.
20
2.2 Design of the pole tip shape to generate a small gradient.
We model this dipole as a conventional electromagnet. Figure 2-1 shows the pole tip
shape of a gradient dipole magnet.
α
hp hv
Figure 2-1
Following procedure shows the derivation of the shape of a gradient magnet pole tip. (Ross
Schlueter’s technical note)
B ∗ = i ( Bo − B ′ z) ( Bo , B′ are real)
(2.1)
B∗ = i F ′
(2.2)
Therefore,
F = Bo z −
B′ 2
z
2
(2.3)
Since
V o ≡ µ o I = Im( F ) = Bo y − B1′ xy ⇒ constant,
(2.4)
 Vo


y pole = 

 Bo − B1′ x 
(2.5)
And
dy pole
dx
=
x =0
Vo B1′
V B′
= o 21 = α
2
(Bo − B1′ x ) Bo
(2.6)
Also,
cosα =
hp
(2.7)
hv
19
II. Gradient Dipole Magnet for the main damping ring.
2.1 Requirements and features
1). Requirements for damping ring dipole magnet are
Goal field at the center (x=0, y=0): 12.01 kG with small gradient of 660.46G/cm.
This gradient is created by angling the pole tips slightly. The distance between the 2 pole
tips is to be 4cm at the center of the pole width. This is shown in detail in the next section.
Length: 48 cm
Tolerances on field shape:
Maximum field variation
dB y
By
= 0.3 % at 1.6 cm circle of radius ( B y is an ideal field.)
Ideal field = pure dipole field + gradient field
2). Electromagnet specs
coil packet size: 5.73 cm × 5.73 cm
number of coil turns = 36
coil current = 543.5 Amps
current density = 729 Amps/cm2
two water circuits are required.
temperature rise at outlet of water circuit = 12.85 oC
3). Gradient dipole magnet (Figure 2-2) as modeled with POISSON meets the field shape
requirement.
Maximum field variation
dB y
By
is about 0.08 % at 1.6 cm circle of radius. Adding shim
around the pole tip can make the magnet smaller.
18
Figure 1-10. Dipole Neo magnet with tuner
17
Figure 1-9. Dipole Ferrite magnet with tuner
16
Figure 1-8. Dipole Neo magnet with shimming (Nominal Bo = 12.987 kG)
15
Figure 1-7. Dipole Neo magnet with shimming (Nominal Bo = 14.43 kG)
14
Figure 1-6. Dipole Neo magnet (Nominal Bo = 12.987 kG)
13
Figure 1-5. Dipole Neo magnet (Nominal Bo = 14.43 kG)
12
Figure 1-4. Dipole Ferrite magnet with shimming (Nominal Bo = 12.987 kG)
11
Figure 1-3. Dipole Ferrite magnet with shimming (Nominal Bo = 14.43 kG)
10
Figure 1-2. Dipole Ferrite magnet (Nominal Bo = 12.987 kG)
9
Figure 1-1. Dipole Ferrite magnet (Nominal Bo = 14.43 kG)
8
and Figure 1-4 are aiming for 12.987 kG of nominal field strength (10 % degradation from
14.43 kG). This 10 % field reduction is made to see how much smaller the magnet gets. So,
comparing Figure 1-1 and Figure 1-2, the height of the magnet is reduced from 46.6” to 34.7”.
The 10 % field degradation makes this difference. The shimming is used in Figure 1-4. The
result shows similar pattern compared to Figure 1-1 and Figure 1-3.
Figure 1-5 and Figure 1-7 show Neo magnet designs. Due to the shimming in Figure
1-7, the dimension is smaller than that of Figure 1-5. Similar pattern can be seen between
Figure 1-6 and Figure 1-8. Figure 1-8 uses the shimming. Also, 10 % reduction of goal field
strength reduces height of magnet from 8.9” (Figure 1-5) to 7.9” (Figure 1-6).
Making an adjustable field strength in the gap.
Figure 1-9 shows a Ferrite magnet with a Neo tuner. The Neo cylindrical rod tuner is
used for generating a field variation. By rotating the tuner, the field at the center location can
be changed by ± 5 %. Figure 1-10 shows a shimmed Neo magnet with Neo tuner. Rotating
tuner makes ± 5 % field variation. Using Neo magnet and adding shim makes a big height
reduction from 31.4” to 7.9”.
Comparing Ferrite magnet and Neo magnet without tuner, there is a significant height
difference. Ferrite magnet has a height of 46.6” (Figure 1-1) and the height of Neo magnet is
8.9” (Figure 1-5).
7
So, it looks like the whole magnet has µ ≈ 1.2. This means that µ is increased by 20 %. To
account this, Hc is degraded by another 20 % to make µ = 1.2, keeping Br same. The next
diagram shows this procedure.
Hc
Br
-12200
12600
20 %
-9760
Normal values for Neo
20 %
10080
Volume effect of temperature compensation
20 %
-7808
Make µ =1.2
So, in PANDIRA program, Hc = -7808 and Br = 10080 are used for Neo. In a similar fashion,
Hc = -2394.3 and Br = 3373.5 are used for Ferrite.
Reduction of field in the gap due to end effects.
End effect loss is calculated using analytical formulae in a spreadsheet. The end effect
loss is a flux loss from the two end faces of a magnet. It depends on the face and length of
magnet. The calculated delta Bgap from the end effect is added back onto the goal field
strength to give a new goal Bgap. We must put enough pm material in the 2-D magnet to
produce the higher Bgap, but the real magnet will only produce the nominal Bgap.
Description of models made incorporating temperature compensation and end effect
Figure 1-1 shows a Ferrite magnet design and Figure 1-3 shows a design of Ferrite
magnet with shimming in order to improve the field quality of the dipole magnet and to
reduce the pole width. The nominal goal field strength at x=0, y=0 is 14.43 kG for both cases.
The required field quality is 0.1% field variation at x=1.2 cm, y=0 from field at the center. As
can be seen in Figure 1-3, with shimming, the width of the magnet is reduced from 2.2” to
1.7”. Consequently, the height of the magnet is also reduced from 46.6” to 43”. Figure 1-2
6
1.2 Details of the PANDIRA Designs
For any hybrid pm magnet there are two features that need to be accounted for in the
2-D PANDIRA computer models. They are (a) the effect of the temperature compensating
material which must be included in the magnet to maintain its integrated strength while the
magnet temperature varies and (b) the effect of flux that escapes out of the ends of the magnet
which normally PANDIRA ignores.
Temperature Compensation.
For all the NLC DR magnets we have tried designs with either Ferrite or Neodymium
Iron Boron (“Neo”) bricks. How much temperature compensation material is needed has to be
worked out empirically for each design on a prototype magnet, in the absence of prototype
magnets we have used percentages of temperature compensation established in real FNAL
permanent magnets built for the Recycler. From these magnets the field strength in the gap
degradations caused by the temperature compensation material are 13.5 % for Ferrite and 20
% for Neo.
One has to be careful in accounting for these substantial percentages in a PANDIRA
model. The following assumptions are made in case of a Neo magnet, Hc and Br are each
decreased by 20 %, this is because adding temperature compensation material makes the
volume of permanent magnet smaller by 20 % for a fixed set of dimensions. Since most
temperature compensating materials have µ ≈ 2, the next process is used for taking account of
µ ≈ 2.
PM
temperature compensation material
(µ =1)
80 %
(µ =2)
20 %
From this figure, the µ relation is
1 x 0.8 + 2 x 0.2 = 1.2.
5
Figure 1-10. Recommended design for transport line dipole magnet of NLC
(Dipole Neo magnet with shimming and tuner, Nominal Bo = 14.43 kG)
4
I. DR Transport Line Dipole Design
1.1 Features and recommendation
Requirements for transport line dipole magnet are
Nominal goal field at the center (x=0, y=0): 14.43kG
Field quality: 0.1% field variation at elliptic region of x=1.2 cm, y=0 from center field
Half gap of the magnet: 0.395” (full gap = 2cm)
Effective length = 0.6m
Tuning requirement: ± 5 %
Several different models were tried using PANDIRA, the details of these models are
given in succeeding pages. We can make a recommendation based on the predictions:
1). Two styles of pm magnets with iron poles were modeled : (a) Ferrite and (b) Neodymium
Iron Boron (“Neo”)
2). Ferrite magnet with shim (Figure 1-3) meets requirements, but is much too tall:
Dimensions: 86” tall, 19.4” width, 6563.94 in3 volume of PM in 22.6” length.
3). Neo magnet with shim (Figure 1-7) meets requirements.
Dimensions: 16.26” tall, 13.2” width, 482.28 in3 volume of PM in 22.6” length.
4).
If we relaxed field strength by 10% and increased length by 10%, to maintain the
integrated strength, the magnet dimensions would become smaller.
Ferrite magnet: 62” tall, 19.4” width, 4833.78 in3 volume of PM in 24.86” length (28 %
height reduction, 26 % reduction of PM volume) (fig. 1-4) STILL TOO TALL!
Neo magnet: 14.7” tall, 13.2” width, 462.89 in3 volume of PM in 24.86” length
(10 % height reduction, 4 % reduction of PM volume) (Figure 1-8)
5). By Neo tuner, there is ± 5 % field variation at the center of magnet.
6). Recommendation: Figure 1-10 is duplicated here to show the recommended model
having reasonable compact dimensions. If radiation damage effects could be minimized or
mitigated the Neo magnet is much preferred.
3
Contents
I. DR Transport Line Dipole Design
3
1.1 Features and recommendation
3
1.2 Details of the PANDIRA Designs
5
II. Gradient Dipole Magnet for the main damping ring
18
2.1 Requirements and features
18
2.2 Design of the pole tip shape to generate a small gradient
19
III. Damping Ring Quadrupole Magnet Design (NLC)
22
3.1 Features and recommendations
22
3.2 2-D Poisson for Permanent Magnets
27
3.3 Temperature Compensation Effects
27
3.4 Tuners
27
3.5 End Effects
29
3.5.1 Three-dimensional modeling of DR quadrupoles
30
3.6 Adding an End Plate on the Magnet - modeling a design feature of the FNAL
Linac PM Quad
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3.7 Demagnetization in the permanent magnet
IV. Electromagnet design and Comparison for NLC Damping Ring Quadrupole
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4.1 Features
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4.2 Electromagnet design
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4.3 Comparison between permanent magnet design and electromagnet design
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LCC-0077
SUMMARY OF LBL/SLAC DESIGN WORK
ON NLC MAGNETS
11/00 – 10/01
Jin-Young Jung
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